具有比例依赖HollingⅢ功能反应和延迟的年龄结构捕食者-猎物模型的渐近分析

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI:10.3934/eect.2022034

Dongxue Yan, Yuan Yuan, Xianlong Fu

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引用次数: 1

摘要

研究了具有年龄结构和两个时滞的无线电依赖捕食者-食饵模型的动力学行为。首先将该模型表述为一个抽象的非密集定义柯西问题，并推导出正平衡点存在的条件。然后，通过确定特征值的分布，分别得到了边界平衡点的全局渐近稳定性和正平衡点的局部渐近稳定性。此外，还证明了在某些条件下，通过Hopf分岔出现非平凡周期振荡现象。最后，给出了一些数值算例来说明所得结果。

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Asymptotic analysis of an age-structured predator-prey model with ratio-dependent Holling Ⅲ functional response and delays

This paper studies the dynamical behavior of a radio-dependent predator-prey model with age structure and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the conditions for existence of the positive equilibrium point are derived. Then, through determining the distribution of eigenvalues, the globally asymptotic stability of the boundary equilibrium and the locally asymptotic stability for the positive equilibrium are obtained, respectively. In addition, it is also shown that a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears under some conditions. Finally, some numerical examples are provided to illustrate the obtained results.

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology